NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs

  • Sepp Hartung
  • André Nichterlein
Conference paper

DOI: 10.1007/978-3-642-30870-3_29

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)
Cite this paper as:
Hartung S., Nichterlein A. (2012) NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs. In: Cooper S.B., Dawar A., Löwe B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg

Abstract

In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrast, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and Müller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter “maximum degree”.

Keywords

graph realization problems combinatorial algorithms parameterized complexity realizing topological orderings 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sepp Hartung
    • 1
  • André Nichterlein
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTechnische Universität BerlinBerlinGermany

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